This is an example of modified version of Sod's problem defined in
[1]} and its solution contains a right shock wave, a right
traveling contact wave and a left sonic rarefaction wave. Transmissive
boundary conditions are taken for numerical evaluation. The solution
is computed up to time \(t=0.2\)  with 200 grid points in space with
the CFL number \(0.5.\)  The density and pressure profile for various
fifth-order WENO schemes are shown in Figure REF  and
Figure REF  respectively against the reference solution
which is calculated with 2000 grid points using WENO-JS scheme.
It is observed that the proposed scheme MWENO-P performs better than
other WENO schemes near the region of contact discontinuity.
<FIGURE><FIGURE>